Approximation from Shift-Invariant Spaces by Integral Operators

We investigate approximation from shift-invariant spaces by using certain integral operators and discuss various applications of this approximation scheme. We assume that our integral operators commute with shift operators and that their kernel functions decay at a polynomial rate. We prove that the...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on mathematical analysis 1997-03, Vol.28 (2), p.481-498
Main Authors: Lei, Junjiang, Jia, Rong-Qing, Cheney, E. W.
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Mathematical functions
Polynomials
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate approximation from shift-invariant spaces by using certain integral operators and discuss various applications of this approximation scheme. We assume that our integral operators commute with shift operators and that their kernel functions decay at a polynomial rate. We prove that the approximation order provided by such an integral operator is m if and only if the integral operator reproduces polynomials of degree up to m-1, where m is a positive integer. Using this result, we characterize the approximation order provided by a finitely generated shift-invariant space whose generators decay in a polynomial rate and have stable shifts. We also review some already well-studied approximation schemes such as projection, cardinal interpolation, and quasi-interpolation by considering them as special cases of integral operators.
ISSN:0036-1410
1095-7154
DOI:10.1137/S0036141095279869